GCF Calculator

Enter two or more integers separated by commas (e.g., 24, 36, 48). The calculator finds the GCF using prime factorization, lists all common factors, and shows the step-by-step working.

Algorithm used: Euclidean Algorithm (also shows prime factorization breakdown for verification).

Example: GCF(24, 36) = 12, because 12 is the largest number that divides both 24 and 36 evenly.

GCF (or GCD) is found by: 1. Prime factorization method: factor each number and multiply the common prime factors raised to their lowest powers. GCF(24, 36): 24 = 2³ × 3, 36 = 2² × 3² → GCF = 2² × 3 = 12

2. Euclidean algorithm: GCF(a, b) = GCF(b, a mod b), recursing until remainder = 0. GCF(24, 36): GCF(36, 24) → GCF(24, 12) → GCF(12, 0) = 12

For multiple numbers: GCF(a, b, c) = GCF(GCF(a, b), c).